Layer 3 switch and ISP Router

I'm having a hard time getting vlan traffic past the L3 switch to the internet. I have a couple of L2 switches and some vlans and a L3 switch. All hosts on all vlans can ping each other, but I cant get them past the L3 switch, only the L3 switch can ping the router which is directly connected.

I thought since it was directly connected it didnt need a route back since it already has one?
10.0.0.0/8 is variably subnetted, 2 subnets, 2 masks
C 10.1.60.0/24 is directly connected, GigabitEthernet0/0
L 10.1.60.2/32 is directly connected, GigabitEthernet0/0

Also, since the VLAN IP addresses did not appear in the "sh ip int brief" command, run the command "sh vlan br" and make sure the VLAN interfaces are not shut. On newly created VLAN's, it is sometimes necessary to issue the "no shut" command for each VLAN.

One odd thing I noticed, the config shows int gi0/1 and gi0/2. But "sh ip int brief" shows int gi0/0 and gi0/1. So perhaps there is a problem with the Packet Tracer config?

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VLAN routing on the L3 switch was working. All VLAN's on the L3 switch were talking to each other, via the L3 switch.

What was not working was the VLAN's could not talk to the router. This was because the router did not have any routes back to the VLAN's on the L3 switch except for the 1 VLAN that was used to interconnect the L3 switch and the router.

tolinrome:

On the L3 device Gi0/2 has "switchport mode trunk". This means it is operating in trunk mode. When a port is in trunk mode:

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